arXiv subjects

Katsuyuki Sugiyama

Publications and source records attributed to Katsuyuki Sugiyama.

At least 19 recordsLinked to original sources

arXiv2023

Photon sphere and quasinormal modes in AdS/CFT

Photon spheres are the characteristic of general black holes, thus are a suitable touchstone for the emergence of gravitational spacetime in the AdS/CFT correspondence. We provide a spectral analysis of an AdS Schwarzschild black hole near its photon sphere. We find that quasinormal modes near the photon sphere reflect the AdS boundary, resulting in a peculiar spectral pattern. Our large angular momentum analysis owes to an analogue to solvable Schrödinger equations such as an inverted harmonic oscillator and the Pöschl-Teller model, with a Dirichlet boundary condition. Through the AdS/CFT dictionary, it predicts the existence of a peculiar subsector in the large angular momentum spectrum of thermal holographic CFTs on a sphere.

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arXiv2020

Supersymmetric indices on $I \times T^2$, elliptic genera and dualities with boundaries

We study three dimensional $\mathcal{N}=2$ supersymmetric theories on $I \times M_2$ with 2d $\mathcal{N}=(0,2)$ boundary conditions at the boundaries $\partial (I \times M_2)=M_2 \sqcup M_2$, where $M_2=\mathbb{C}$ or $ T^2$. We introduce supersymmetric indices of three dimensional $\mathcal{N}=2$ theories on $I \times T^2$ that couple to elliptic genera of 2d $\mathcal{N}=(0,2)$ theories at the two boundaries. We evaluate the $I \times T^2$ indices in terms of supersymmetric localization and study dualities on the $I \times M_2$. We consider the dimensional reduction of $I \times T^2$ to $I \times S^1$ and obtain the localization formula of 2d $\mathcal{N}=(2,2)$ supersymmetric indices on $I \times S^1$. We illustrate computations of open string Witten indices based on gauged linear sigma models. Correlation functions of Wilson loops on $I \times S^1$ agree with Euler pairings in the geometric phase and also agree with cylinder amplitudes for B-type boundary states of Gepner models in the Landau-Ginzburg phase.

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arXiv2020

Localization of 3d $\mathcal{N}=2$ Supersymmetric Theories on $S^1 \times D^2$

We study three dimensional $\mathcal{N}=2$ supersymmetric Chern-Simons-Matter theories on the direct product of a circle and a two dimensional hemisphere ($S^1 \times D^2$) with specified boundary conditions by the method of localization. We construct boundary interactions to cancel the supersymmetric variation of the three dimensional superpotential term and the Chern-Simons term and show inflows of the bulk-boundary anomalies. It finds that the boundary conditions induce two dimensional $\mathcal{N}=(0,2)$ type supersymmetry on the boundary torus. We also study the relation between the 3d-2d coupled partition function of our model and three dimensional holomorphic blocks.

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arXiv2018

Equivariant U(N) Verlinde algebra from Bethe/Gauge correspondence

We compute the topological partition function (twisted index) of $\mathcal{N}=2$ $U(N)$ Chern-Simons theory with an adjoint chiral multiplet on $Σ_g \times S^1$. The localization technique shows that the underlying Frobenius algebra is the equivariant Verlinde algebra which is obtained from the canonical quantization of the complex Chern-Simons theory regularized by $U(1)$ equivariant parameter $t$. Our computation relies on a Bethe/Gauge correspondence which allows us to represent the equivariant Verlinde algebra in terms of the Hall-Littlewood polynomials $P_λ(x_B, t)$ with a specialization by Bethe roots $x_B$ of the $q$-boson model. We confirm a proposed duality to the Coulomb branch limit of the lens space superconformal index of four dimensional $\mathcal{N}=2$ theories for $SU(2)$ and $SU(3)$ with lower levels. In $SU(2)$ case we also present more direct computation based on Jeffrey-Kirwan residue operation.

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arXiv2006

Superconformal Symmetry in Linear Sigma Model on Supermanifolds

We consider a gauged linear sigma model in two dimensions with Grassmann odd chiral superfields. We investigate the Konishi anomaly of this model and find out the condition for realization of superconformal symmetry on the world-sheet. When this condition is satisfied, the theory is expected to flow into conformal theory in the infrared limit. We construct superconformal currents explicitly and study some properties of this world-sheet theory from the point of view of conformal field theories.

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arXiv2005

Gauged Linear Sigma Model on Supermanifold

We formulate a gauged linear sigma model on a supermanifold. The structure of classical vacua is investigated and one-loop corrections are calculated for an auxiliary D-field. We find out a constraint for the one-loop divergence to vanish, which is consistent with a Ricci flatness condition for the supermanifold. Two types of D-branes are obtained by analysing supersymmetric boundary conditions. We also provide extensions to a non-abelian gauged linear sigma model and a (0,2) supersymmetric model.

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arXiv2004

Construction of Supergravity Backgrounds with a Dilaton Field

A new class of non-compact Kahler backgrounds accompanied by a non-constant dilaton field is constructed as a supergravity solution. It is interpreted as a complex line bundle over a base manifold comprising of a combination of arbitrary coset spaces, and also includes the case of Calabi-Yau manifolds. The resulting backgrounds have U(1) isometry. We consider N=2 supersymmetric sigma-models on them, and derive a non-Kahlerian solution by U(1) duality transformation, which preserves N=2 supersymmetry.

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arXiv2004

N=2 Supersymmetric Sigma Models and D-branes

We study D-branes of N=2 supersymmetric sigma models. Supersymmetric nonlinear sigma models with 2-dimensional target space have D0,D1,D2-branes, which are realized as A-,B-type supersymmetric boundary conditions on the worldsheet. When we embed the models in the string theory, the Kahler potential is restricted and leads to a 2-dim black hole metric with a dilaton background. The D-branes in this model are susy cycles and consistent with the analysis of conjugacy classes. The generalized metrics with U(n) isometry is proposed and dynamics on them are realized by linear sigma models. We investigate D-branes of the linear sigma models and compare the results with those in the nonlinear sigma models.

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arXiv2003

Partition Function and Open/Closed String Duality in Type IIA String Theory on a PP-wave

We discuss partition functions of N=(4,4) type IIA string theory on the pp-wave background. This theory is shown to be modular invariant. The boundary states are constructed and possible D-brane instantons are classified. Then we calculate cylinder amplitudes in both closed and open string descriptions and check the open/closed string duality. Furthermore we consider general properties of modular invariant partition functions in the case of pp-waves.

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arXiv2002

BPS Conditions of Supermembrane on the PP-wave

We study the BPS conditions in the closed supermembranes on the maximally supersymmetric pp-wave background. In particular, the 1/2 and 1/4 BPS states are discussed in detail. Moreover, we comment on the zero-modes in the invariant mass formulae of the theory.

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arXiv2002

Ground State of Supermembrane on PP-wave

We consider the ground state of supermembrane on the maximally supersymmetric pp-wave background by using the quantum-mechanical procedure of de Wit-Hoppe-Nicolai. In the pp-wave case the ground state has non-trivial structure even in the zero-mode Hamiltonian, which is identical with that of superparticles on the pp-wave and resembles supersymmetric harmonic oscillators. The supergravity multiplet in the flat case is splitting with a certain energy difference. We explicitly construct the unique supersymmetric ground-state wave function of the zero-mode Hamiltonian, which is obviously normalizable. Moreover, we discuss the nonzero-mode Hamiltonian and construct an example for the ground-state wave function with a truncation of the variables. This special solution seems non-normalizable but its L^2-norm can be represented by an asymptotic series.

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arXiv2002

Type IIA String and Matrix String on PP-wave

We study type IIA string theories on the pp-waves with 24 supercharges. The type IIA pp-wave backgrounds are derived from the maximally supersymmetric pp-wave solution in eleven dimensions through the toroidal compactification on the spatial isometry directions. The associated actions of type IIA strings are obtained by using these metrics and other background fields of the type IIA supergravities on the one hand. On the other hand, we derive these theories from D=11 supermembrane on the pp-wave via double dimensional reduction for the spatial isometry directions. The resulting actions agree with those of type IIA strings obtained in the study of the supergravities. Also, the action of the matrix string is written down. Moreover, the quantization of closed and open strings is discussed. In particular, we study Dp-branes allowed in one of the type IIA theories.

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arXiv2002

Giant Graviton and Quantum Stability in Matrix Model on PP-wave Background

We study classical solutions in Berenstein-Maldacena-Nastase (BMN) matrix model. A supersymmetric (1/2 BPS) fuzzy sphere is one of the classical solutions and corresponds to a giant graviton. We also consider other classical solutions, such as non-supersymmetric fuzzy sphere and harmonic oscillating gravitons. Some properties of oscillating gravitons are discussed. In particular, oscillating gravitons turn into usual supergravitons in the limit mu -> 0. Moreover, we calculate the one-loop effective action around the supersymmetric fuzzy sphere by the use of the background field method and show the quantum stability of the giant graviton. Also, the instability of the non-supersymmetric fuzzy sphere is proven.

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arXiv2002

Supermembrane on the PP-wave Background

We study the closed and open supermembranes on the maximally supersymmetric pp-wave background. In the framework of the membrane theory, the superalgebra is calculated by using the Dirac bracket and we obtain its central extension by surface terms. The result supports the existence of the extended objects in the membrane theory in the pp-wave limit. When the central terms are discarded, the associated algebra completely agrees with that of Berenstein-Maldacena-Nastase matrix model. We also discuss the open supermembranes on the pp-wave and elaborate the possible boundary conditions.

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arXiv2002

Coset Construction of Noncompact Spin(7) and G_2 CFTs

We provide a new class of exactly solvable superconformal field theories that corresponds to type II compactification on manifolds with exceptional holonomies. We combine N=1 Liouville field and N=1 coset models and construct modular invariant partition functions of strings moving on these manifolds. The resulting theories preserve spacetime supersymmetry. Also we explicitly construct chiral currents in these models to realize consistent string theories.

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arXiv2001

Cascade of Special Holonomy Manifolds and Heterotic String Theory

We investigate hetrotic string theory on special holonomy manifolds including exceptional holonomy G_2 and Spin(7) manifolds. The gauge symmetry is F_4 in a G_2 manifold compactification, and so(9) in a Spin(7) manifold compactification. We also study the cascade of the holonomies: so(8) > Spin(7) > G_2 > su(3) > su(2). The differences of adjoining groups are described by Ising, tricritical Ising, 3-state Potts and u(1) models. These theories are essential for spacetime supersymmetries and gauge group enhancements. As concrete examples, we construct modular invariant partition functions and analyze their massless spectra for G_2 and Spin(7) orbifolds. We obtain the relation between topological numbers of the manifolds and multiplicities of matters in specific representations.

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arXiv2001

D-branes on a Noncompact Singular Calabi-Yau Manifold

We investigate D-branes on a noncompact singular Calabi-Yau manifold by using the boundary CFT description, and calculate the open string Witten indices between the boundary states. The B-type D-branes turn out to be characterized by the properties of a compact positively curved manifold. We give geometric interpretations to these boundary states in terms of coherent sheaves of the manifold.

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arXiv2000

Comments on Central Charge of Topological Sigma Model with Calabi-Yau Target Space

We study a central charge Z of a one parameter family of Calabi-Yau d-fold embedded in CP^{d+1}. For a d-fold case, we construct the Z concretely and analyze charge vectors of D-branes and intersection forms of associated cycles. We find the charges are described as some kinds of Mukai vectors. They are represented as products of Chern characters of coherent sheaves restricted on the Calabi-Yau hypersurfaces and square roots of A-roof genera of the d-folds. By combining results of the topological sigma model and the data of the CFT calculations in the Gepner model, we find that the Z is determined and is specified by a set of integers. It labels boundary states in special classes where associated states are represented as tensor products of boundary states for constituent minimal models. The Z has a moduli parameter t that describes a deformation of a moduli space in the open string channel with B-type boundary conditions. Also monodromy matrices and homology cycles are investigated.

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